Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  albitr Structured version   Unicode version

Theorem albitr 36397
Description: Theorem *10.301 in [WhiteheadRussell] p. 151. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
albitr  |-  ( ( A. x ( ph  <->  ps )  /\  A. x
( ps  <->  ch )
)  ->  A. x
( ph  <->  ch ) )

Proof of Theorem albitr
StepHypRef Expression
1 bitr 713 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  ch )
)  ->  ( ph  <->  ch ) )
21alanimi 1684 1  |-  ( ( A. x ( ph  <->  ps )  /\  A. x
( ps  <->  ch )
)  ->  A. x
( ph  <->  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ wa 370   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678
This theorem depends on definitions:  df-bi 188  df-an 372
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator